This reprint is focuses on distributions and moments and publish papers on the theory and applications of probability and statistics. Papers include original results of symmetric random walks and their characterization, stochastic processes, stochastic integrals, martingales, probability inequalities, statistics parameter estimation, stochastic differential equations, fractional Brownian motions, continuous time random walk models, anomalous diffusion models, Black-Scholes models, Monte Carlo methods, etc. This Special Issue is focused on concepts and techniques and is oriented toward a broad spectrum of applied mathematics and sciences. Focused review articles reviewed the state of the art and identify upcoming challenges and promising solutions for the scientific community.